Question

Please help with this question, thank you!!!​

Answer 1

a) (i) (A ∪ B) ∩ C = {1, 3, 5}

a) (ii) (A ∪ C) ∩ B = {2, 4}

b) (i) P ∩ (Q ∪ Q') = P

b) (ii) (P ∩ P') ∪ Q = Q

Explanation:

A ∪ B means the union of A and B, so the numbers that are in A or B (or both).

A ∩ B means the intersection of A and B, so the numbers that are in both A and B.

Part (a)

Given sets:

• A = {1, 2, 3, 4, 5}
• B = {2, 4, 6, 8}
• C = {1, 3, 5, 7}

Question (i)

(A ∪ B) ∩ C = ( {1, 2, 3, 4, 5} ∪ {2, 4, 6, 8} ) ∩ {1, 3, 5, 7}

= {1, 2, 3, 4, 5, 6, 8} ∩ {1, 3, 5, 7}

= {1, 3, 5}

Question (ii)

(A ∪ C) ∩ B = ( {1, 2, 3, 4, 5} ∪ {1, 3, 5, 7} ) ∩ {2, 4, 6, 8}

= {1, 2, 3, 4, 5, 7} ∩ {2, 4, 6, 8}

= {2, 4}

Part (b)

Question (i)

`\begin{aligned} \sf P \cap (Q \cup Q') & = \sf P \cap \mathbb{U}\\& = \sf P\end{aligned}`

Question (ii)

`\begin{aligned} \sf (P \cap P')\cup Q & = \sf \emptyset \cup Q\\& = \sf Q\end{aligned}`